Package smile.manifold

Class LaplacianEigenmap

java.lang.Object

smile.manifold.LaplacianEigenmap

public class LaplacianEigenmap
extends Object

Laplacian Eigenmaps. Using the notion of the Laplacian of the nearest neighbor adjacency graph, Laplacian Eigenmaps computes a low dimensional representation of the dataset that optimally preserves local neighborhood information in a certain sense. The representation map generated by the algorithm may be viewed as a discrete approximation to a continuous map that naturally arises from the geometry of the manifold.

The locality preserving character of the Laplacian Eigenmaps algorithm makes it relatively insensitive to outliers and noise. It is also not prone to "short-circuiting" as only the local distances are used.

See Also:

• IsoMap
• LLE

• References

  1. Mikhail Belkin and Partha Niyogi. Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering. NIPS, 2001.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final record	LaplacianEigenmap.Options	Laplacian Eigenmaps hyperparameters.

Method Summary

Modifier and Type	Method	Description
static double[][]	fit(double[][] data, LaplacianEigenmap.Options options)	Laplacian Eigenmaps with Gaussian kernel.
static double[][]	fit(NearestNeighborGraph nng, LaplacianEigenmap.Options options)	Laplacian Eigenmaps with Gaussian kernel.
static <T> double[][]	fit(T[] data, Distance<T> distance, LaplacianEigenmap.Options options)	Laplacian Eigenmaps with discrete weights.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

fit

public static double[][] fit(double[][] data,
 LaplacianEigenmap.Options options)

Laplacian Eigenmaps with Gaussian kernel.

Parameters:

data - the input data.

options - the hyperparameters.

Returns:

the embedding coordinates.

fit

public static <T> double[][] fit(T[] data,
 Distance<T> distance,
 LaplacianEigenmap.Options options)

Laplacian Eigenmaps with discrete weights.

Type Parameters:

T - the data type of points.

Parameters:

data - the input data.

distance - the distance function.

options - the hyperparameters.

Returns:

the embedding coordinates.

fit

public static double[][] fit(NearestNeighborGraph nng,
 LaplacianEigenmap.Options options)

Laplacian Eigenmaps with Gaussian kernel.

Parameters:

nng - the k-nearest neighbor graph.

options - the hyperparameters.

Returns:

the embedding coordinates.